The computation of Buehler confidence limits

In medicine and industry, small sample size often arises owing to the high test cost. Then exact confidence inference is important. Buehler confidence limit is a kind of exact confidence limit for the function of parameters in a model. It can be always defined if the order in sample space is given. But the computing problem is often difficult, especially for the cases with high dimension parameter or with incomplete data. This paper presents an algorithm to compute the Buehler confidence limits by EM algorithm. This is the first-time usage of EM algorithm on Buehler confidence limits, but the algorithm is often used for maximum likelihood estimate in literatures. Three computation examples are given to illustrate the method.     

灰色正项几何规划研究

In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this model can be regarded as interval grey numbers. When the model contains grey numbers, it is hard for common programming method to solve them. By combining the common programming model with the grey system theory, and using some analysis strategies, a model of grey polynomial geometric programming, a model of θpositioned geometric programming and their quasi-optimum solution or optimum solution are put forward. At the same time, we also developed an algorithm for the problem. This approach brings a new way for the application research of geometric programming. An example at the end of this paper shows the rationality and feasibility of the algorithm.     

Parameter estimation of the WMTD model

The MTD （mixture transition distribution） model based on Weibull distribution （WMTD model） is proposed in this paper, which is aimed at its parameter estimation. An EM algorithm for estimation is given and shown to work well by some simulations. And bootstrap method is used to obtain confidence regions for the parameters. Finally, the results of a real example--predicting stock prices--show that the WMTD model proposed is able to capture the features of the data from thick-tailed distribution better than GMTD （mixture transition distribution） model.     

A new generalized linear exponential distribution and its applications

A new generalized linear exponential distribution （NCLED） is considered in this paper which can be deemed as a new and more flexible extension of linear exponential distribution. Some statistical properties for the NGLED such as the hazard rate function, moments, quantiles are given. The maximum likelihood estimations （MLE） of unknown parameters are also discussed. A simulation study and two real data analyzes are carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.     

A RECURSIVE ALGORITHM AND ITS CONVERGENCE FOR PARAMETER ESTIMATION OF CONVOLUTION MODEL

In this article, the problem on the estimation of the convolution model parameters is considered. The recursive algorithm for estimating model parameters is introduced from the orthogonal procedure of the data, the convergence of this algorithm is theoretically discussed, and a sufficient condition for the convergence criterion of the orthogonal procedure is given. According to this condition, the recursive algorithm is convergent to model wavelet A- = （1, α1,..., αq）.     

A skew–normal mixture of joint location,scale and skewness models

Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models: a skew–normal mixture of joint location,scale and skewness models to analyze the heteroscedastic skew–normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation–Maximization(EM) algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index(BMI) data are presented.     

Empirical likelihood inference for estimating equation with missing data

In this article, empirical likelihood inference for estimating equation with missing data is considered. Based on the weighted-corrected estimating function, an empirical log-likelihood ratio is proved to be a standard chi-square distribution asymptotically under some suitable conditions. This result is different from those derived before. So it is convenient to construct confidence regions for the parameters of interest. We also prove that our proposed maximum empirical likelihood estimator θ is asymptotically normal and attains the semiparametric efficiency bound of missing data. Some simulations indicate that the proposed method performs the best.     

Binomial proportion estimation in longitudinal data with non-ignorable non-response

Non-random missing data poses serious problems in longitudinal studies. The binomial distribution parameter becomes to be unidentifiable without any other auxiliary information or assumption when it suffers from ignorable missing data. Existing methods are mostly based on the log-linear regression model. In this article, a model is proposed for longitudinal data with non-ignorable non-response. It is considered to use the pre-test baseline data to improve the identifiability of the post-test parameter. Furthermore, we derive the identified estimation (IE), the maximum likelihood estimation (MLE) and its associated variance for the post-test parameter. The simulation study based on the model of this paper shows that the proposed approach gives promising results.     

AN ADAPTIVE MEMBRANE ALGORITHM FOR SOLVING COMBINATORIAL OPTIMIZATION PROBLEMS

Membrane algorithms （MAs）, which inherit from P systems, constitute a new parallel and distribute framework for approximate computation. In the paper, a membrane algorithm is proposed with the improvement that the involved parameters can be adaptively chosen. In the algorithm, some membranes can evolve dynamically during the computing process to specify the values of the requested parameters. The new algorithm is tested on a well-known combinatorial optimization problem, the travelling salesman problem. The em-pirical evidence suggests that the proposed approach is efficient and reliable when dealing with 11 benchmark instances, particularly obtaining the best of the known solutions in eight instances. Compared with the genetic algorithm, simulated annealing algorithm, neural net-work and a fine-tuned non-adaptive membrane algorithm, our algorithm performs better than them. In practice, to design the airline network that minimize the total routing cost on the CAB data with twenty-five US cities, we can quickly obtain high quality solutions using our algorithm.     

ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA

In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.     

基于删失数据的指数威布尔分布最大似然估计的新算法

本文讨论了指数威布尔分布当观测数据是删失数据情形时参数的最大似然估计问题.因为删失数据是一种不完全数据,我们利用EM算法来计算参数的近似最大似然估计.由于EM算法计算的复杂性,计算效率也不理想.为了克服牛顿-拉普森算法和EM算法的局限性,我们提出了一种新的方法.这种方法联合了指数威布尔分布到指数分布的变换和等效寿命数据的技巧,比牛顿-拉普森算法和EM算法更具有操作性.数据模拟讨论了这一方法的可行性.为了演示本文的方法,我们还提供了一个真实寿命数据分析的例子.     

Pareto-Geometric分布

本文提出了一种具有单调失效率的新型寿命分布, 即由Pareto分布和Geometric分布生成的两参数的Pareto-Geometric分布, 研究了该分布的各种性质和参数极大似然估计的存在唯一性, 并应用 EM 算法得到了参数的极大似然估计值和相应的渐近方差、协方差.     

基于分组数据的回归系数的估计

本文讨论了如何去解决基于分组数据下的回归系数的估计问题.本文所讨论的基于分组数据下的回归模型与经典回归模型的差异在于因变量的观测值为分组数据,即我们只知道它落于事先确定的一组区间中的某一区间,而不知道它的具体值;而经典回归模型的因变量观测值则是一个确定的数值.我们用MLE去估计回归系数,但是此时的MLE无显式解,所以寻找一个合适的迭代算法就成了问题的关键.我们选择利用Bayes计算方法中的EM算法来获得估计量的迭代公式.随机模拟显示了所得估计的有效性.     

一个新的具有单调降失效率的寿命分布

本文由Pareto分布和Logarithmic分布"混合"生成两参数具有单调降失效率的新型寿命分布,研究了该分布的矩、熵、失效率函数、平均剩余寿命和参数的极大似然估计,应用EM算法求参数的极大似然估计,进行了数值模拟.     

Em algorithm of the truncated multinormal distribution with linear restriction on the variables

A new expectation-maximization (EM) algorithm is proposed to estimate the parameters of the truncated multinormal distribution with linear restriction on the variables. Compared with the generalized method of moments (GMM) estimation and the maximum likelihood estimation (MLE) for the truncated multivariate normal distribution, the EM algorithm features in fast calculation and high accuracy which are shown in the simulation results. For the real data of the national college entrance exams (NCEE), we estimate the distribution of the NCEE examinees’ scores in Anhui, 2003, who were admitted to the university of science and technology of China (USTC). Based on our analysis, we have also given the ratio truncated by the NCEE admission line of USTC in Anhui, 2003.     

缺失数据下含几何分布的对数线性模型的EM算法

本文研究缺失数据下对数线性模型参数的极大似然估计问题.通过Monte-Carlo EM算法去拟合所提出的模型.其中,在期望步中利用Metropolis-Hastings算法产生一个缺失数据的样本,在最大化步中利用Newton-Raphson迭代使似然函数最大化.最后,利用观测数据的Fisher信息得到参数极大似然估计的渐近方差和标准误差.     

离子通道的混合密度参数估计与状态判别

本文针对多电导水平离子通道的由多个正态分布加权组成的混合分布特点,用EM迭代算法对混合分布中的参数进行极大似然估计,并在此基础上,利用混合分布中最可能的成分判断通道状态,从而还原通道潜在信号,克服了离子通道分析软件PCLAMP中参数估计与状态还原的缺陷。     

基于数据分组与右删失情形下对数正态分布的参数估计

本文研究了对数正态分布数据在分组与删失情形下参数的估计问题. 一是给出未知参数的极大似然估计存在且唯一的充要条件. 二是利用EM算法对参数值进行了估计.     

Statistical Analysis in Constant-Stress Accelerated Life Tests for Generalized Exponential Distribution Based on Adaptive Type-II Progressive Hybrid Censored Data

Based on adaptive type-II progressive hybrid censored data statistical analysis for constant-stress accelerated life test (CS-ALT) with products' lifetime following two-parameter generalized exponential (GE) distribution is investigated. The estimates of the unknown parameters and the reliability function are obtained through a new method combining the EM algorithm and the least square method. The observed Fisher information matrix is achieved with missing information principle, and the asymptotic unbiased estimate (AUE) of the scale parameter is also obtained. Confidence intervals (CIs) for the parameters are derived using asymptotic normality of the estimators and the percentile bootstrap (Boot-p) method. Finally, Monte Carlo simulation study is carried out to investigate the precision of the point estimates and interval estimates, respectively. It is shown that the AUE of the scale parameter is better than the corresponding two-step estimation, and the Boot-p CIs are more accurate than the corresponding asymptotic CIs.     

Statistical inference for coherent systems with Weibull distributed component lifetimes under complete and incomplete information

Point estimators for the parameters of the component lifetime distribution in coherent systems are evolved assuming to be independently and identically Weibull distributed component lifetimes. We study both complete and incomplete information under continuous monitoring of the essential component lifetimes. First, we prove that the maximum likelihood estimator (MLE) under complete information based on progressively Type‐II censored system lifetimes uniquely exists and we present two approaches to compute the estimates. Furthermore, we consider an ad hoc estimator, a max‐probability plan estimator and the MLE for the parameters under incomplete information. In order to compute the MLEs, we consider a direct maximization of the likelihood and an EM‐algorithm–type approach, respectively. In all cases, we illustrate the results by simulations of the five‐component bridge system and the 10‐component parallel system, respectively.